Please enjoy this week’s AstroInfo, courtesy of Jeremy Higgins. He wrote our planetarium program on calendars (Ancient Skies, Ancient Eyes) that ran in conjunction with the Dead Sea Scrolls exhibit a couple years ago. Recently, probably inspired by the lack of Sun in Seattle, he’s been looking into calendars and tracking time a bit more, and found some interesting things. It’s a great article – and the short of it is: it’s pretty hard to make a well balanced calendar based on the Sun or the Moon, especially if you care about keeping dates and holidays in the same part of the year. Here it is, enjoy!

The Winter Solstice has arrived and passed. The days will begin to lengthen. The Sun won’t be setting at just after 4pm for very much longer. The Solstice is when the Sun stops rising and setting further to the South every day, instead beginning it’s 6 month long march to its northernmost rising and setting points. I am going through my yearly surprise at just how early this seasonal change causes The Sun to rise and set every day; we have sunset as early as 4:20pm in Seattle! The Solstices have been an important time of the year for cultures all around the world. It’s a good time to define just what we mean when we talk about the year.

What is a Year?

Generally, when we talk about a “year” we might assume that we are talking about the same thing. We might assume that we are discussing the 365.2425 days that it requires the Earth to recreate its path around the Sun. After all, this cycle gives us convenient points to mark out our seasonal changes. We can talk about the beginning of our seasons happening at certain points throughout the year. It’s very convenient. Except that for billions of people around the world, this calendar doesn’t mark their most important dates. The year one might assume we are referring to would be a year as marked out by the Gregorian calendar. This calendar was decreed by the Pope in 1582 for Catholic countries. The previous Julian calendar, itself an improvement on the Roman calendar, lost a day every 128 years. Additionally, in the beginning of its usage, the people responsible for implementing this calendar incorrectly added a leap day every 3 years. Whoops. That mistake having been resolved by skipping leap years for a while, there was an eleven day discrepancy. Someone would have to give up those days!

What’s the Problem?

As we can see, we begin to encounter calendar issues that could become very contentious. There is mythical rioting associated with the “stolen” eleven days in Europe. As we head back further, we start to see that the calendar reflects religious beliefs as well as civic needs. We can then move on to problems with holidays (holy days) arriving on the wrong days.

In the planetarium, when discussing the years, I ask people about different lengths of time. The conversation generally goes like this:

Me: What’s a year?Visitors: 365 days… and, oh yeah, we add a day every four years.Me: Right, it’s 365 and a quarter. Add those quarters up every four years and you get a dollar- or a day. Now, what’s a month?Visitors: 30 days! 31 days! Er, 28 days! I mean sometimes 29 days!Me: Wow, how can a month be all those different numbers of days? Aren’t units of time supposed to be the same? Isn’t a minute always 60 seconds? Isn’t an hour always 60 minutes…?Visitors: Um, well… Don’t confuse me! Burn the witch! [that would be me they’re interested in burning]

Month – Moonth

I ask them to think about the word: month. If you stare at it for a long time, you might see an extra ‘o’ in the middle- moonth. Our moon has various cycles, but the one that is most visible from Earth is that of its phases. The moon takes roughly 29.5 days to go from one phase all the way back to that phase again. We can see that this cycle is close to the 30 (or so) day month. Now we see that we can create a calendar by sticking 12 of these nearly 30 day cycles together. However, to create a calendar like this, we’re going to have to give up those half days. You can’t have a half day on a calendar. It’s not like you’d get to go home early or something.

So, let’s make this Lunar calendar out of alternating months of 29 days and 30 days. If you’re scoring at home, you say, “Hey Guest AstroInfo guy, you are going to get really messed up, because if you string 12 of those moonths together, you’re going to end up with 354 days!” You’re right. Imagine you go 10 years with a calendar that is strictly a lunar calendar. You would end up more than 100 days off of the Tropical Year. (The Tropical Year is the year that is described when we talk about the Earth making one full revolution around the Sun, not the year you get to spend in Costa Rica). We could also call this a solar year. If this were to happen, we’d end up with winter holidays in the summer. Let’s burn the Yule Log, it’s only 75 degrees outside. (It would be the opposite in the Southern hemisphere).

In my opinion, the cycles of the moon are far easier and more convenient to follow. You can break your time increments up into smaller chunks. You can see that the moon made it into 28 locations in the sky throughout this time period. You can break the entire thing up into quarters. It’s pretty flexible. Still, you are left with the problem of the 11 day difference. Well, because many cultures have holidays with specific seasonal meaning, there would need to be a way to adjust for this problem.

Fixing the Lunar/Solar Mismatch

If we look specifically at the Hebrew calendar, we can see a solution. A “Leap Month,” or intercalary month, is added every 2 or 3 years to give 7 leap months every 19 years. It is a very convenient way of adjusting a lunar calendar to coincide with the mechanics of the Tropical Year. This creates a “lunisolar” calendar.

Here is where we see some area where disagreement may occur. If your calendar is one in which the days are being consistently switched around, you may end up with your holy days falling on the wrong kinds of days. According to the authors of the Dead Sea Scrolls, this was a problem. Part of the reason that the group who wrote the Dead Sea Scrolls separated themselves from the other Jewish people at the time was so that they could practice the use of their own calendar. The Dead Sea Scrolls describe a calendar which more closely aligns with a solar year. It allowed for holy days to fall on their correct kinds of days every year. Although, I must add that the year was described as being 364 days long, and there is no information as to what was done to correct for the missing day(s).

Who Uses a Lunar Calendar?

There are billions of people around the world who follow a lunar calendar. There is a Hindu lunar calendar, a Jewish lunar calendar, a Chinese lunar calendar… There are definitely other cultures which use a lunar calendar at least as historical perspective. The Islamic lunar calendar is a little different in that it specifically forbids the use of an intercalary month. Because of this, an important date on the Islamic calendar will be earlier by 11 days every year.

Calendars from Long Ago

We can meander back further to the creators of the first roughly 365 day calendar. The Egyptians used a calendar that was 365 days, but it was only indirectly based on the path of the Sun in the sky. This calendar relied upon the star we currently call Sirius. They watched this star for the time when it would first become visible in the sky before dawn. This rising of Sirius happened to roughly coincide with the flooding of the Nile. These ancient people watched the same thing happen every year- star rises, Nile floods, star rises, Nile floods. This is the kind of pattern that allowed the ancient Egyptians to create a calendar that roughly coincided with the 365 day calendar. One interesting note about this Egyptian calendar is that it had 36 “weeks” of 10 days each. Obviously, that ends up being short of their own 365 day period. What did they do with 5 extra days every year? What do you do when you have extra days? You have parties and festivals, right? So did the ancient Egyptians.

Clearly, this only scratches the surface of the change in calendrical thinking over the millennia. I invite you to research further points of interest in calendars.

2 Responses to “Calendrical Conundrums”

Hi Alice,
This is an excellent handout. It led me to check what I wrote about the calendar in my Planets paper, and it turns out that I misremembered it when I was telling you about it. The Gregorian calendar gains one day every 3200 years, not 2800 years. I’m not sure what this has to do with all those leap seconds, since if we want to avoid being ahead by one day in the year 3200 we should be subtracting seconds, not adding them. Maybe I should do some research and find out what all these leap seconds are about. Anyway, here’s what I wrote about the calendar year:

calendar year. The calendar which is in use throughout most of the world is the Gregorian calendar, which was instituted by Pope Gregory XIII in 1582. According to the Gregorian calendar, every year divisible by 4 is a leap year. However, every year divisible by 100 is not a leap year. But every year divisible by 400 is a leap year after all. Therefore 1900 (divisible by 100 but not 400) had 365 days, whereas 2000 (divisible by 100 and 400) had 366 days. Based on the Gregorian calendar, the year has an average of 365.2425 days (365 days 5 hours 49 minutes 12 seconds). This is 27 seconds longer than the tropical year and means that the Gregorian calendar gains 1 day every 3200 years. Note: The number 3200 is not an approximation. 3200 times 27 seconds equals 86,400 seconds, which is the number of seconds in a day.